When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
Answer:
So in other words, each week he works, he gets an additional $10, to add to his collection of really $75.
Step-by-step explanation:
so, he has $85 in savings, and that he has the opportunity to gain allowance by the following function of 10(x-1).
total funds(x) = 85 + 10(x-1)
T(x) = 85 + 10x - 10
T(x) = 10x + 75
1.6 hours
152 km total divided by her speed, 95 km/h =1.6
For this question, you simply multiply 32.4 by 12.7 to get the number of miles that Jennie can drive. The answer is 411.48, choice c.
Hope this helps!
